Question

a rectilinear motion of a particle is defined by v3=x3. determine the velocity and acceleration at x=8m

Answer 1

The velocity is 8 m/s and acceleration is 8
`m/s^(2)`

Step-by-step explanation:

The motion of the particle is given by:

`v^(3)`=
`x^(3\\)`

or, v= x .................................1

substitute x= 8m,

v= 8 m/s

Now differentiate it with respect to time (t),

`(dv)/(dt)` =
`(dx)/(dt)`

or,
`(dv)/(dt)` = v

∴
`(dv)/(dt)` = v

now substitute the value of v from equation 1,

`(dv)/(dt)` = x

now at, x= 8

`(dv)/(dt)` = 8

∴
`(dv)/(dt)` = 8
`m/s^(2)`

As

`(dv)/(dt)` = acceleration

So the acceleration of the particle at x=8m is 8
`m/s^(2)` .